The finite-time Lyapunov exponent (FTLE) has become a standard tool for analyzing unsteady flow phenomena, partly since its ridges can be interpreted as Lagrangian coherent structures (LCS). While there are several definitions for ridges, a particular one called second derivative ridges has been introduced in the context of LCS, but subsequently received criticism from several researchers for being over-constrained. Among the critics are Norgard and Bremer [Physica D 2012.05.006], who suggest furthermore that the widely used definition of height ridges was a part of the definition of second derivative ridges, and that topological separatrices were ill-suited for describing ridges. We show that (a) the definitions of height ridges and second derivative ridges are not directly related, and (b) there is an interdisciplinary consensus throughout the literature that topological separatrices describe ridges. Furthermore, we provide pointers to practically feasible and numerically stable ridge extraction schemes for FTLE fields.


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